Asymptotic theory and econometric practice

The classical paradigm of asymptotic theory employed in econometrics presumes that model dimensionality, p, is fixed as sample size, n, tends to inifinity. Is this a plausible meta-model of econometric model building? To investigate this question empirically, several meta-models of cross-sectional wage equation models are estimated and it is concluded that in the wage-equation literature at least that p increases with n roughly like n1/4, while that hypothesis of fixed model dimensionality of the classical asymptotic paradigm is decisively rejected. The recent theoretical literature on `large-p' asymptotics is then very briefly surveyed, and it is argued that a new paradigm for asymptotic theory has already emerged which explicitly permits p to grow with n. These results offer some guidance to econometric model builders in assessing the validity of standard asymptotic confidence regions and test statistics, and may eventually yield useful correction factors to conventional test procedures when p is non-negligible relative to n.